Prediction of the mean value of the dependent variable y for values of the independent variables x 1, x 2, . . . , x q that are outside the experimental range is called extrapolation of data.
What is extrapolation of data?In statistics and mathematics, especially in the branch of data-science it is quite common to use a range of values from a parameter to predict the values of the dependent variable.
One of the most common applications of this is regression equations, when pairs of one of the independent variables with the dependent variable are used to predict the dependent variable.
In the case of this problem, we want to predict the dependent variable, but with values that are outside the experimental range, hence we extrapolate the data inside the experimental range for values that are outside the experimental range.
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Please help me with this. Show the solution as well. Thank you
Step-by-step explanation:
any ordered pair is a solution, if we can use its coordinates in the equation, and the equation stays true.
for x - 3y = 6
1. (3, -1)
3 - 3×-1 = 6
3 + 3 = 6
6 = 6
true, this is a solution.
2. (0, 2)
0 - 3×2 = 6
-6 = 6
false, this is not a solution.
3. (3, 1)
3 - 3×1 = 6
3 - 3 = 6
0 = 6
false, this is not a solution.
Maria buys n pencils that cost p each, she pays with a $y note find in terms of n, p and y, the amount of change maria recieves. give your answer in cents
The amount of change Maria receives is 100y - np
What is Conversion rate ?
A conversion rate is the ratio between two currencies, most commonly used in foreign exchange markets, which designates how much of one currency is needed to exchange for the equivalent value of another currency.
Given,
The cost of each pencil is = p
Maria buys = n pencils
so, the cost of n pencils is = np
She pays for the n pencils is = $y
Now, in question given that we need to find answer in cents
so, We know 1$ = 100 cents
By that, $y = 100y
Maria received the change is = 100y - np
Therefore, the amount of change Maria receives is 100y - np
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The quadratic 3x^2+4x-9 has two real roots. What is the sum of the squares of these roots? Express your answer as a common fraction in lowest terms.
If the quadratic [tex]3x^2[/tex]+4x-9 =0 has two real roots, then the sum of the square of the these roots is 7.77
The polynomial is [tex]3x^2[/tex]+4x-9 =0
Here,
a = 3
b = 4
c = -9
Here the quadratic equation
= [tex]\frac{-b+/-\sqrt{b^2-4ac} }{2a}[/tex]
Substitute the values in the quadratic equation
= [tex]\frac{-4+/-\sqrt{4^2-4(3)(-9)} }{2(3)}[/tex]
The result will be
= [tex]\frac{-2+/-\sqrt{31} }{3}[/tex]
Therefore, the roots are
[tex]\frac{-2+\sqrt{31} }{3}[/tex] and [tex]\frac{-2-\sqrt{31} }{3}[/tex]
Square of the first root = [tex](\frac{-2+\sqrt{31} }{3} )^{2}[/tex]
= 1.414
Square of the second root = [tex](\frac{-2-\sqrt{31} }{3} )^2[/tex]
= 6.363
The sum of the square of the roots = 1.414+6.363
= 7.77
Hence, if the quadratic [tex]3x^2[/tex]+4x-9 =0 has two real roots, then the sum of the square of the these roots is 7.77
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Two exponential functions, f(x) and g(x), are graphed on the same coordinate plane. Graph of f of x equals 2 to the x power going through points 0 comma 1 and 1 comma 2 and graph of g of x equals 2 to the x power plus 4 going through points 0 comma 5 and 1 comma 6. What effect does adding 4 to the parent function have on the transformed function? a Adding 4 to the parent function shifts the function down four units. b Adding 4 to the parent function shifts the function up four units. c Adding 4 to the parent function shifts the function right four units. d Adding 4 to the parent function shifts the function left four units.
Answer:
b Adding 4 to the parent function shifts the function up four units.
Step-by-step explanation:
The original function is y(x) = 2^x
Adding four is y(x) = 2^x + 4
We've simply told y to take whatever value is generated for x and add four to it.
So the new value for the same x would have 4 added to y: (x,y+4),
Point (1,2) would shift to point (1,6).
Adding four to the parent function will shift the entire graph up by 4. See ate attached graph.
A triangle has been plotted on the coordinate plane.
Which series of transformations will result in Point B” being the greatest distance from the x-axis.
A - reflect over the x-axis then rotate 90° clockwise
B - rotate 80° clockwise then reflect over the line x= -1
C - rotate 90° clockwise then translate following the rule (x+1, y-1)
D - translate (x+1,y-1) then reflect over the y-axis
REALLY NEED THIS
When a point is reflected across the x-axis, the x-coordinate remains unchanged, but the y-coordinate is assumed to be the additive inverse. Point (x, yreflection )'s across the x-axis is (x, -y). A point's reflection over the y axis is shown. The reflection rule over the y axis is (x,y)(x,y).
What exactly is a coordinate plane?A coordinate plane is a two-dimensional plane formed by two number lines intersecting. One of these number lines is a horizontal number line known as the x-axis, and the other is a vertical number line known as the y-axis.
1) Determine the absolute value of x1(y2-y3) + x2(y3-y1) + x3(y1-y2).
2) The area of the triangle is calculated by dividing this value by two.
3) Use our area of a triangle with coordinates calculator to confirm this result.
The coordinate plane can be used to draw lines and points. This system allows us to visually describe algebraic relationships, as well as create and interpret algebraic concepts.
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Over the last four months, your investment lost
10%, 20%, 30%, and then 40%. What percent
of the original investment do you have left?
Answer:
30.24%
Step-by-step explanation:
Each time you lose x%, you end up with 1 - 0.01x.
For example, if you lose 10% of an amount, you end up with 1 - 0.01(10), or 0.9 times the original amount.
Let's say you started with x.
You lost 10%. Now you have 0.9x.
Then you lost 20% of the remaining amount. Now you have 0.8(0.9x).
Then you lost 30% of the remaining amount. Now you have 0.7(0.8)(0.9x).
Finally you lost 40% of the remaining amount. Now you have 0.6(0.7)(0.8)(0.9x).
The final amount you have is
0.6(0.7)(0.8)(0.9x) = 0.3024x = 30.24% of x
Answer: 30.24%
Refer to Expression 1 and Expression 2.
Expression 1
6-7-3².9+43
r:
Expression 2
5+4+2+6-2-2-1
(a) What is the value of Expression 1?
(b) Insert parentheses in Expression 2 so that it has a value of 19. Then show why your expression has a
value of 19.
a) Value of Expression 1 is 29.833.
b) After inserting the parentheses the expression is (5+4) * 2 + 6 -2 * 2 - 1.
The order of operations to solve in expression 1 is:
First parenthesis, then multiplication and division, and then addition and subtraction.
So, the expression is:
6 × 7 - 3 ÷ 2 × 9 + 4 ÷ 3
First, solve division and then multiplication:
= 42 - 1.5 × 9 + 1.34
= 42 - 13.5 + 1.34
= 29.84
b) Because the parenthesis is the initial action, so insert it in 5+4 which provides the following result:
(5 + 4) × 2 + 6 - 2 × 2 - 1
First, calculate the parenthesis, then the multiplication and division, and finally perform addition and subtraction:
= (9) × 2 + 6 - 4 - 1
= 18 + 6 - 4 - 1
= 19
The final value is 19.
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HELP PLEASE!!!!!!!
A rectangle is 32ft by 8ft. Ross dilated the rectangle and the dimensions of the image were 80ft by 20ft. What was the scale factor used?
The scale factor of the dilation = 2.5
The original dimensions of the rectangle:
Length = 32 ft
Width = 8 ft
The dimensions of the rectangle after dilation:
Length = 80 ft
Width = 20 ft
Dilation is a transformation where the dimensions of the figure is enlarged by multiplying with a number. This number multiplied with all dimensions of the original figure is called its scale factor.
So the new dimension of the figure will be scale factor times the original dimensions of the figure.
Thus the scale factor can be defined as the ratio of larger dimension to the smaller dimension of a figure.
Hence the scale factor used here is the ratio of new length to the original length or the ratio of new width to the original width of the rectangle.
That is, scale factor = 80/32 = 20/8 = 2.5
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Evaluate compositions of function. Let f(x) = 3x + 2, g(x) = -x2, and h(x) = x-2/5. Find the indicated value. (SHOW WORK PLEASE))
The indicated numeric values for the composite functions are given as follows:
1. f(g(-3)) = -25.
2. g(f(2)) = -64.
3. h(f(-5)) = -3.
4. g(g(-3)) = -81.
What is the composite function of f(x) and g(x)?The composite function of f(x) and g(x) is according to the following rule:
(f ∘ g)(x) = f(g(x)).
It means that the output of the inside function serves as the input for the outside function. Hence, to calculate f(g(-3)), for example, we calculate g(-3), then we calculate the numeric value of function f(x) at x = g(-3).
For this problem, the functions are given as follows:
f(x) = 3x + 2.g(x) = -x².h(x) = (x - 2)/5.For item 1, the numeric values are found as follows:
g(-3) = -(-3)² = -9.f(g(-3)) = f(-9) = 3(-9) + 2 = -27 + 2 = -25.For item 2, the numeric values are found as follows:
f(2) = 3(2) + 2 = 6 + 2 = 8.g(f(2)) = g(8) = -(8)² = -64.For item 3, the numeric values are found as follows:
f(-5) = 3(-5) + 2 = -15 + 2 = -13.h(f(-5)) = h(-13) = (-13 - 2)/5 = -3.For item 4, the numeric values are found as follows:
g(-3) = -(-3)² = -9.g(g(-3)) = g(-9) = (-9)² = -81.More can be learned about composite functions at https://brainly.com/question/10687170
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What is the slope of this image?? I NEED HELP
Answer:
Positive, so the answer would be y=4/2 or 2. y=2x-4
Step-by-step explanation:
Slope formula y=mx+b
The mx is the rise/ over run
The b is the y-intercept
You can check in the end by checking so to see if the rise over the run is correct
Also, you can check the b by looking at the y-intercept, which is -4
Hope this helps!
Two parallel lines are cut by a transversal. Suppose <1 and <2 are alternate interior angles and that m<1=4(x+2) and m<2=2x+24. What is the m<2?
The value of m∠2 will be equal to 40°.
Transversal may be defined as a line which cuts two different lines which lie on the same plane at two different points. Alternate interior angles may be defined as the angles which are formed when a transversal cut the two different lines. These angles lie on the interior of the parallel lines, but they are on the opposite side of the transversal. If two parallel lines are cut by a transversal, then their alternate interior angles are equal. Thus, m∠1 = m∠2
4(x + 2) = 2x + 24
4x + 8 = 2x + 24
2x = 16
=> x = 16/2
=> x = 8
Now, m∠2 = 2x + 24
m∠2 = 2×8 + 24
m∠2 = 40° which is the required answer.
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i'll give brainliest
Answer:
-40
Step-by-step explanation:
10/1*(-4) Set up equation
10/1 * -4 Open up parentheses
10/1 =10 Next, divide 10 by 1
10*-4 Now, multiply 10 and -4
-40 Answer
Answer:
-40
Step-by-step explanation:
Given expression
[tex]\dfrac{10}{1} \cdot (-4)[/tex]
When dividing and multiplying, follow the order of operations and work from left to right.
Divide the numbers
When dividing anything by 1, the quotient is the numerator:
[tex]\implies \dfrac{10}{1} \cdot (-4)=10 \cdot (-4)[/tex]
Multiply the numbers
When multiplying a positive number by a negative number, the product is always negative:
[tex]\implies 10 \cdot (-4)=-40[/tex]
Look at this set of ordered pairs:
(7, -17)
(5,3)
(7,3)
Is this relation a function?
yes
no
The given relation is not a function.
What is function?
A function is a relationship between inputs where each input is related to exactly one output.
Given that, (7, -17) , (5. 3) , (7, 3)
Here 7 is connected with two elements i.e. -17 and 3 but the condition of a function is that one element must be related to only one element of another set.
Hence, the given relation is not a function.
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3.7416573868 to nearest tenth
Explanation:
The tenths decimal place is right after the decimal point
7 is in the tenths place
The digit just to the right of 7 is 4
Since the 4 is not 5 or larger, this means we erase everything after the 7 and go with 3.7
If we had something like 3.76, then the 7 bumps up to 8 to get 3.8
Measure of angle 1 = 110 degrees. You only need to type 110.
The unknown angles are as follows:
∠1 = 110°∠2 = 70°∠3 = 110°∠4 = 70°∠5 = 110°∠6 = 70°∠7 = 110°∠8 = 70°How to find angles?When parallel lines are cut by a transversal line, angle relationships are formed such as corresponding angles, linear angles, alternate angles etc.
Therefore,
∠1 = 110 degrees(given)
∠2 = 180 - 110 (sum of angles on a straight line)
∠2 = 70°
∠3 = ∠1 (vertically opposite angles)
Vertically opposite angles are congruent.
Therefore,
∠3 = 110°
∠2 = ∠4 (vertically opposite angles)
∠4 = 70°
∠1 = ∠5 (corresponding angles)
Corresponding angles are congruent
∠5 = 110°
∠6 = ∠4(alternate angles)
Alternate angles are congruent.
∠6 = 70°
∠1 = ∠7 (alternate exterior angles)
∠7 = 110°
∠2 = ∠8(alternate exterior angles)
∠8 = 70°
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i'll give you brainliest
-53 = 8y + 4y - 17 solve for y and simplify as much as possible
Answer:
y = -3
Step-by-step explanation:
-53 = 8y + 4y - 17
combine y terms on right side:
-53 = 12y - 17
add 17 to both sides:
-53 + 17 = 12y - 17 + 17
-36 = 12y
divide both sides by 12:
-36/12 = 12y/12
y = -3
A star shape is made out of 5 congruent triangles. the peak of 1 triange is 25°. what are the sizes of the base angles?
Answer:
77.5
Step-by-step explanation:
180-25=155
155/2=77.5
a certain bacteria doubles every 2 seconds. Starting from a single bacterium, how many bacteria will be there after 20 seconds?
The answer will de 10 bacterias
Answer: 1024
Step-by-step explanation: Since there's only 1 bacteria at first, we can just do 2^x. x being the amount of time divided by the amount of time between each time it doubles. Since the bacteria doubles every 2 seconds, and 20/2 = 10 we get 2^10 which is 1024.
Find the value of each variable
Answer:
x = 58°
y = 74°
z = 106°
w = 42°
Step-by-step explanation:
Finding the value of unknown variables:
x + 32° = 90°
x = 90 - 32
[tex]\sf \boxed{\bf x = 58^\circ}[/tex]
x + y + 48 = 180 {Angle sum property of triangle}
58 + y + 48 = 180
y + 106 = 180
y = 180 - 106
[tex]\sf \boxed{\bf y = 74\°}[/tex]
y + z = 180 {Linear pair}
74 + z = 180
z = 180 - 74
[tex]\sf \boxed{\bf z = 106\°}[/tex]
32 +z + w = 180 {Angle sum property of triangle}
32 + 106 +w = 180
138 + w = 180
w = 180 - 138
[tex]\sf \boxed{\bf w = 42\°}[/tex]
Please I need help right now
A mathematical function is a mathematical relationship where each input value (x) has a unique output value (y), which means that it is a relationship where every individual value for the independent variable always results in a specific predictable value for the dependent variable.
What is meant by mathematical function?A mathematical function is a mathematical relationship where each input value (x) has a unique output value (y), which means that it is a relationship where every individual value for the independent variable always results in a specific predictable value for the dependent variable.
The exact same number of elements from Y are assigned to each element of X via a mathematical function from a set X to a set Y. The sets X and Y are collectively referred to as the function's domain and codomain, respectively.
A mathematical phrase, rule, or law that establishes the relationship between two variables, one of which is independent and the other dependent (the dependent variable)
The complete question is:
What is a mathematical function? After studying the vending machine examples, write a definition that communicates precisely what it means for a mathematical relationship to be a function.
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PLS HELP!!!
Zane deposited $3,000 in an account earning 11% interest compound annually. To the nearest cent, how much will he have in 4 years?
Answer:4554.21
Step-by-step explanation:
Jai is 1.45 meters tall. At 11 a.m., he measures the length of a tree's shadow to be
39.55 meters. He stands 34.1 meters away from the tree, so that the tip of his shadow
meets the tip of the tree's shadow. Find the height of the tree to the nearest
hundredth of a meter.
오ㅜ
39.55 m-
(Diagram is not to scale.)
1.45 m
34.1 m-
By using triangles laws, we know that the height of the tree is 8.42 meters.
What are triangles?A polygon with three edges and three vertices is called a triangle. It is one of the fundamental geometric shapes. Triangle ABC is the designation for a triangle with vertices A, B, and C. In Euclidean geometry, any three points that are not collinear produce a distinct triangle and a distinct plane.So, 1.45 m is Joshua's height.
Tree shadow length: L=31.65 mJoshua's distance from the tree is 26.2 meters.We must ascertain the tree's height.
BC = 26.2 mBD = 31.65mCD = BD-BCCD = 31.65-26.2=5.45 mEC = 1.45 mThe right triangles are all alike.
The ratio of the corresponding sides is equal when two triangles are comparable.
△ABD ≈ △ECDAB/EC = BD/CDNow, put values as follows:
AB/1.45 = 31.65/5.45AB = 31.65 × 1.45/5.45AB = 8.42mTherefore, by using triangles laws, we know that the height of the tree is 8.42 meters.
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The correct form of the question is given below:
Joshua is 1.45 meters tall. At 2 p.m., he measures the length of a tree's shadow to be 31.65 meters. He stands 26.2 meters away from the tree so that the tip of his shadow meets the tip of the tree's shadow. Find the height of the tree to the nearest hundredth of a meter.
The team's engagement score was 5.20 this month. the score has been improving at a rate of 8% per month. what was the score 3 months ago? 1.60 3.95 4.13 4.78 5.12
The score 3 months ago was 4.130.
What is rate of increase?
Rate of increase is defined the change in rate that describes how one quantity changes in relation to another quantity.
Assume the score 3 months ago was x. This means that the above can be expressed as:
Current score = x × ( 1 + rate) ^ number of months
5.20= x(1+8%)^3
5.20 = x(1.259)
x= 5.20/1.259
x= 4.130
therefore, the score was 4.130
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Johnathan is hosting a barbeque for 7 of his friends. He wants to buy twice as many sausages as burgers and the same number of buns as sausages and burgers combined.
Buns come in a packet of 6
Sausages come in a pack of 10
Burgers come in a pack of 8.
What is the smallest number of packets of buns that Johnathan could buy?
The smallest number of packets of buns that Jonathan could buy is 4.
What is an expression?An expression is a combination of terms that are combined by using mathematical operations such as subtraction, addition, multiplication, and division.
We have,
Buns come in a packet of 6
Sausages come in a pack of 10
Burgers come in a pack of 8.
Sausage = 2 x burgers ____(1)
Buns = Sausages + Burgers _____(2)
The smallest number of packets of buns can be calculated when only one packet of Burgers is bought.
So,
Burgers = 1 pack = 8
From (1) and (2),
Sausage = 2 x 8 = 16
Buns = 16 + 8 = 24
Buns = 24
This can be put in 4 packets.
Thus,
The smallest number of packets of buns that Jonathan could buy is 4.
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Boris's art class is 8 hours long. How long is his class in minutes?
Answer:
480 minutes
Step-by-step explanation:
that's your answer
Answer:
480 minutes.
Step-by-step explanation:
8×60=480.
How many subsets does the set (1,2,3) have
Answer:
Answer down below!
Step-by-step explanation:
The set (1, 2, 3) would have 8 sets in total
Which of the following values are in the range of the function graphed below?
Check all that apply.
The range of the function is 1
As seen by the graph in the following figure
As can be seen, x's value falls between
nonetheless, y is equal to 1 for all values of x.
This holds true regardless of x's value.
Consequently, the function's range is 1.
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Find the range, variance & standard deviation of the following sample dataset. Round all answers to the nearest tenth.
The following data represent the number of students from each school that attended a debate tournament: 75, 47, 50, 71, 64, 50, 52, 56, 53, 47, 55
Answer:
The range is 28
The variance is 90.855
The mean is 56.36
The median is 53
The sample standard deviation is 9.532
Step-by-step explanation:
Question 9
The preimage of M(-3,-5) under a translation is M'(6, -1).
Using the same translation, find the image of B', if B is (3,-2).
B'
By using the same translation applied to point M, the image of point B' is equal to (12, 2).
What is a translation?In Geometry, a translation can be defined as a type of transformation which moves every point of a geometric figure (object) in the same direction, as well as for the same distance.
Since the x-coordinate moved from a negative to a positive sign, we know that point M was translated to the right and then shifted down because it moved from a negative to a negative sign on the y-coordinate.
Next, we would determine the translation rule that was applied to point M:
(x, y) → (x + n, y - z)
-3 + n = 6
n = 6 + 3
n = 9.
-5 - z = -1
z = -5 + 1
z = -4
Now, we can determine the image of B':
(x, y) → (x + n, y - z)
Point B (3, -2) → Point B' (3 + 9, -2 - (-4)) = (12, 2).
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